// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"

template<typename MatrixType>
void
product_extra(const MatrixType& m)
{
	typedef typename MatrixType::Scalar Scalar;
	typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
	typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
	typedef Matrix<Scalar, Dynamic, Dynamic, MatrixType::Flags & RowMajorBit> OtherMajorMatrixType;

	Index rows = m.rows();
	Index cols = m.cols();

	MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols),
			   mzero = MatrixType::Zero(rows, cols), identity = MatrixType::Identity(rows, rows),
			   square = MatrixType::Random(rows, rows), res = MatrixType::Random(rows, rows),
			   square2 = MatrixType::Random(cols, cols), res2 = MatrixType::Random(cols, cols);
	RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
	ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
	OtherMajorMatrixType tm1 = m1;

	Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>(), s3 = internal::random<Scalar>();

	VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(), m1 * m2.adjoint().eval());
	VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
	VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2, m1.adjoint().eval() * m2);
	VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2, (s1 * m1.adjoint()).eval() * m2);
	VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2, (numext::conj(s1) * m1.adjoint()).eval() * m2);
	VERIFY_IS_APPROX(m3.noalias() = (-m1.adjoint() * s1) * (s3 * m2), (-m1.adjoint() * s1).eval() * (s3 * m2).eval());
	VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2, (s2 * m1.adjoint() * s1).eval() * m2);
	VERIFY_IS_APPROX(m3.noalias() = (-m1 * s2) * s1 * m2.adjoint(), (-m1 * s2).eval() * (s1 * m2.adjoint()).eval());

	// a very tricky case where a scale factor has to be automatically conjugated:
	VERIFY_IS_APPROX(m1.adjoint() * (s1 * m2).conjugate(), (m1.adjoint()).eval() * ((s1 * m2).conjugate()).eval());

	// test all possible conjugate combinations for the four matrix-vector product cases:

	VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2), (-m1.conjugate() * s2).eval() * (s1 * vc2).eval());
	VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()), (-m1 * s2).eval() * (s1 * vc2.conjugate()).eval());
	VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),
					 (-m1.conjugate() * s2).eval() * (s1 * vc2.conjugate()).eval());

	VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),
					 (s1 * vc2.transpose()).eval() * (-m1.adjoint() * s2).eval());
	VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),
					 (s1 * vc2.adjoint()).eval() * (-m1.transpose() * s2).eval());
	VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),
					 (s1 * vc2.adjoint()).eval() * (-m1.adjoint() * s2).eval());

	VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),
					 (-m1.adjoint() * s2).eval() * (s1 * v1.transpose()).eval());
	VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),
					 (-m1.transpose() * s2).eval() * (s1 * v1.adjoint()).eval());
	VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
					 (-m1.adjoint() * s2).eval() * (s1 * v1.adjoint()).eval());

	VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2), (s1 * v1).eval() * (-m1.conjugate() * s2).eval());
	VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2), (s1 * v1.conjugate()).eval() * (-m1 * s2).eval());
	VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),
					 (s1 * v1.conjugate()).eval() * (-m1.conjugate() * s2).eval());

	VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
					 (-m1.adjoint() * s2).eval() * (s1 * v1.adjoint()).eval());

	// test the vector-matrix product with non aligned starts
	Index i = internal::random<Index>(0, m1.rows() - 2);
	Index j = internal::random<Index>(0, m1.cols() - 2);
	Index r = internal::random<Index>(1, m1.rows() - i);
	Index c = internal::random<Index>(1, m1.cols() - j);
	Index i2 = internal::random<Index>(0, m1.rows() - 1);
	Index j2 = internal::random<Index>(0, m1.cols() - 1);

	VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0, j, m1.rows(), c),
					 m1.col(j2).adjoint().eval() * m1.block(0, j, m1.rows(), c).eval());
	VERIFY_IS_APPROX(m1.block(i, 0, r, m1.cols()) * m1.row(i2).adjoint(),
					 m1.block(i, 0, r, m1.cols()).eval() * m1.row(i2).adjoint().eval());

	// test negative strides
	{
		Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic>> map1(
			&m1(rows - 1, cols - 1), rows, cols, Stride<Dynamic, Dynamic>(-m1.outerStride(), -1));
		Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic>> map2(
			&m2(rows - 1, cols - 1), rows, cols, Stride<Dynamic, Dynamic>(-m2.outerStride(), -1));
		Map<RowVectorType, Unaligned, InnerStride<-1>> mapv1(&v1(v1.size() - 1), v1.size(), InnerStride<-1>(-1));
		Map<ColVectorType, Unaligned, InnerStride<-1>> mapvc2(&vc2(vc2.size() - 1), vc2.size(), InnerStride<-1>(-1));
		VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
		VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
		VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(),
						 m1.reverse() * m2.reverse().adjoint());
		VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
		VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
		VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
		VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
		VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
	}

	// regression test
	MatrixType tmp = m1 * m1.adjoint() * s1;
	VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);

	// regression test for bug 1343, assignment to arrays
	Array<Scalar, Dynamic, 1> a1 = m1 * vc2;
	VERIFY_IS_APPROX(a1.matrix(), m1 * vc2);
	Array<Scalar, Dynamic, 1> a2 = s1 * (m1 * vc2);
	VERIFY_IS_APPROX(a2.matrix(), s1 * m1 * vc2);
	Array<Scalar, 1, Dynamic> a3 = v1 * m1;
	VERIFY_IS_APPROX(a3.matrix(), v1 * m1);
	Array<Scalar, Dynamic, Dynamic> a4 = m1 * m2.adjoint();
	VERIFY_IS_APPROX(a4.matrix(), m1 * m2.adjoint());
}

// Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947
void
mat_mat_scalar_scalar_product()
{
	Eigen::Matrix2Xd dNdxy(2, 3);
	dNdxy << -0.5, 0.5, 0, -0.3, 0, 0.3;
	double det = 6.0, wt = 0.5;
	VERIFY_IS_APPROX(dNdxy.transpose() * dNdxy * det * wt, det * wt * dNdxy.transpose() * dNdxy);
}

template<typename MatrixType>
void
zero_sized_objects(const MatrixType& m)
{
	typedef typename MatrixType::Scalar Scalar;
	const int PacketSize = internal::packet_traits<Scalar>::size;
	const int PacketSize1 = PacketSize > 1 ? PacketSize - 1 : 1;
	Index rows = m.rows();
	Index cols = m.cols();

	{
		MatrixType res, a(rows, 0), b(0, cols);
		VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(rows, cols));
		VERIFY_IS_APPROX((res = a * a.transpose()), MatrixType::Zero(rows, rows));
		VERIFY_IS_APPROX((res = b.transpose() * b), MatrixType::Zero(cols, cols));
		VERIFY_IS_APPROX((res = b.transpose() * a.transpose()), MatrixType::Zero(cols, rows));
	}

	{
		MatrixType res, a(rows, cols), b(cols, 0);
		res = a * b;
		VERIFY(res.rows() == rows && res.cols() == 0);
		b.resize(0, rows);
		res = b * a;
		VERIFY(res.rows() == 0 && res.cols() == cols);
	}

	{
		Matrix<Scalar, PacketSize, 0> a;
		Matrix<Scalar, 0, 1> b;
		Matrix<Scalar, PacketSize, 1> res;
		VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize, 1));
		VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize, 1));
	}

	{
		Matrix<Scalar, PacketSize1, 0> a;
		Matrix<Scalar, 0, 1> b;
		Matrix<Scalar, PacketSize1, 1> res;
		VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize1, 1));
		VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize1, 1));
	}

	{
		Matrix<Scalar, PacketSize, Dynamic> a(PacketSize, 0);
		Matrix<Scalar, Dynamic, 1> b(0, 1);
		Matrix<Scalar, PacketSize, 1> res;
		VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize, 1));
		VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize, 1));
	}

	{
		Matrix<Scalar, PacketSize1, Dynamic> a(PacketSize1, 0);
		Matrix<Scalar, Dynamic, 1> b(0, 1);
		Matrix<Scalar, PacketSize1, 1> res;
		VERIFY_IS_APPROX((res = a * b), MatrixType::Zero(PacketSize1, 1));
		VERIFY_IS_APPROX((res = a.lazyProduct(b)), MatrixType::Zero(PacketSize1, 1));
	}
}

template<int>
void
bug_127()
{
	// Bug 127
	//
	// a product of the form lhs*rhs with
	//
	// lhs:
	// rows = 1, cols = 4
	// RowsAtCompileTime = 1, ColsAtCompileTime = -1
	// MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5
	//
	// rhs:
	// rows = 4, cols = 0
	// RowsAtCompileTime = -1, ColsAtCompileTime = -1
	// MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1
	//
	// was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using
	// the max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.

	Matrix<float, 1, Dynamic, RowMajor, 1, 5> a(1, 4);
	Matrix<float, Dynamic, Dynamic, ColMajor, 5, 1> b(4, 0);
	a* b;
}

template<int>
void
bug_817()
{
	ArrayXXf B = ArrayXXf::Random(10, 10), C;
	VectorXf x = VectorXf::Random(10);
	C = (x.transpose() * B.matrix());
	B = (x.transpose() * B.matrix());
	VERIFY_IS_APPROX(B, C);
}

template<int>
void
unaligned_objects()
{
	// Regression test for the bug reported here:
	// http://forum.kde.org/viewtopic.php?f=74&t=107541
	// Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.
	// There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,
	// memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.
	for (int m = 450; m < 460; ++m) {
		for (int n = 8; n < 12; ++n) {
			MatrixXf M(m, n);
			VectorXf v1(n), r1(500);
			RowVectorXf v2(m), r2(16);

			M.setRandom();
			v1.setRandom();
			v2.setRandom();
			for (int o = 0; o < 4; ++o) {
				r1.segment(o, m).noalias() = M * v1;
				VERIFY_IS_APPROX(r1.segment(o, m), M * MatrixXf(v1));
				r2.segment(o, n).noalias() = v2 * M;
				VERIFY_IS_APPROX(r2.segment(o, n), MatrixXf(v2) * M);
			}
		}
	}
}

template<typename T>
EIGEN_DONT_INLINE Index
test_compute_block_size(Index m, Index n, Index k)
{
	Index mc(m), nc(n), kc(k);
	internal::computeProductBlockingSizes<T, T>(kc, mc, nc);
	return kc + mc + nc;
}

template<typename T>
Index
compute_block_size()
{
	Index ret = 0;
	ret += test_compute_block_size<T>(0, 1, 1);
	ret += test_compute_block_size<T>(1, 0, 1);
	ret += test_compute_block_size<T>(1, 1, 0);
	ret += test_compute_block_size<T>(0, 0, 1);
	ret += test_compute_block_size<T>(0, 1, 0);
	ret += test_compute_block_size<T>(1, 0, 0);
	ret += test_compute_block_size<T>(0, 0, 0);
	return ret;
}

template<typename>
void
aliasing_with_resize()
{
	Index m = internal::random<Index>(10, 50);
	Index n = internal::random<Index>(10, 50);
	MatrixXd A, B, C(m, n), D(m, m);
	VectorXd a, b, c(n);
	C.setRandom();
	D.setRandom();
	c.setRandom();
	double s = internal::random<double>(1, 10);

	A = C;
	B = A * A.transpose();
	A = A * A.transpose();
	VERIFY_IS_APPROX(A, B);

	A = C;
	B = (A * A.transpose()) / s;
	A = (A * A.transpose()) / s;
	VERIFY_IS_APPROX(A, B);

	A = C;
	B = (A * A.transpose()) + D;
	A = (A * A.transpose()) + D;
	VERIFY_IS_APPROX(A, B);

	A = C;
	B = D + (A * A.transpose());
	A = D + (A * A.transpose());
	VERIFY_IS_APPROX(A, B);

	A = C;
	B = s * (A * A.transpose());
	A = s * (A * A.transpose());
	VERIFY_IS_APPROX(A, B);

	A = C;
	a = c;
	b = (A * a) / s;
	a = (A * a) / s;
	VERIFY_IS_APPROX(a, b);
}

template<int>
void
bug_1308()
{
	int n = 10;
	MatrixXd r(n, n);
	VectorXd v = VectorXd::Random(n);
	r = v * RowVectorXd::Ones(n);
	VERIFY_IS_APPROX(r, v.rowwise().replicate(n));
	r = VectorXd::Ones(n) * v.transpose();
	VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());

	Matrix4d ones44 = Matrix4d::Ones();
	Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();
	VERIFY_IS_APPROX(m44, Matrix4d::Constant(4));
	VERIFY_IS_APPROX(m44.noalias() = ones44 * Matrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(m44.noalias() = ones44.transpose() * Matrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(m44.noalias() = Matrix4d::Ones() * ones44, Matrix4d::Constant(4));
	VERIFY_IS_APPROX(m44.noalias() = Matrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));

	typedef Matrix<double, 4, 4, RowMajor> RMatrix4d;
	RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();
	VERIFY_IS_APPROX(r44, Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = ones44 * Matrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = ones44.transpose() * Matrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = Matrix4d::Ones() * ones44, Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = Matrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = ones44 * RMatrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = ones44.transpose() * RMatrix4d::Ones(), Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = RMatrix4d::Ones() * ones44, Matrix4d::Constant(4));
	VERIFY_IS_APPROX(r44.noalias() = RMatrix4d::Ones() * ones44.transpose(), Matrix4d::Constant(4));

	//   RowVector4d r4;
	m44.setOnes();
	r44.setZero();
	VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);
	r44.setZero();
	VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);
	r44.setZero();
	VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);
	r44.setZero();
	VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);
}

EIGEN_DECLARE_TEST(product_extra)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(product_extra(
			MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_2(product_extra(
			MatrixXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_2(mat_mat_scalar_scalar_product());
		CALL_SUBTEST_3(product_extra(MatrixXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2),
											   internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2))));
		CALL_SUBTEST_4(product_extra(MatrixXcd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2),
											   internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2))));
		CALL_SUBTEST_1(zero_sized_objects(
			MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	}
	CALL_SUBTEST_5(bug_127<0>());
	CALL_SUBTEST_5(bug_817<0>());
	CALL_SUBTEST_5(bug_1308<0>());
	CALL_SUBTEST_6(unaligned_objects<0>());
	CALL_SUBTEST_7(compute_block_size<float>());
	CALL_SUBTEST_7(compute_block_size<double>());
	CALL_SUBTEST_7(compute_block_size<std::complex<double>>());
	CALL_SUBTEST_8(aliasing_with_resize<void>());
}
